Fast Parameter Learning in Adaptive Systems

Abstract

Adaptive control pertains to the control of dynamic systems exposed to parametric uncertainties in real-time with guarantees of stability and control goals of tracking. A central part of adaptive control is parameter estimation. Real-time adaptive control requires parameter estimation to occur quickly and accurately. This thesis is dedicated to fast parameter estimation in adaptive identification and control of linear dynamic systems with time-invariant and time-varying parameters.

Several algorithms for fast parameter convergence are proposed in this thesis, both in discrete and continuous time, for adaptive identification and control. Three different algorithms are proposed for discrete-time systems: the first introduces a time-varying gain, the second is based on a second-order tuner that combines acceleration and momentum-like terms, and the third combines the first two. In each case, a guarantee of boundedness is established with no requirements of input excitation. With input excitation, parameter convergence is established for constant parameters, with the convergence proven to be exponential when the excitation is persistent. For continuous-time systems, the thesis consists of two contributions, both in the context of adaptive control. The first is a proof of parameter convergence for a new class of adaptive controllers for a class of nonlinear dynamic systems with multiple inputs, with adaptive control in the inner loop and reinforcement learning in the outer loop. This convergence is shown to be exponential when persistent excitation conditions are satisfied. Finally, stability and parameter convergence are established for adaptive control of a class of linear time-varying systems whose states are not accessible for measurement. Here, the thesis introduces yet another adaptive algorithm that combines a standard gradient-descent approach with that based on an integral error. When the time variations are known, it is shown that parameter convergence can occur; when the time variations are unknown, the parameter estimates are shown to converge to a compact set.